 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2019

Paper 211

Apply <Itô formula> to $V(t,S_t)$. Its Brownian coefficient is
$$
\sigma S_t\frac{\partial V}{\partial s}(t,S_t).
$$
The self-financing portfolio's Brownian coefficient is $\pi_t\sigma S_t$. Since $S_t\sigma>0$, equality of the two value processes forces
$$
\boxed{\pi_t=\widetilde V(t,S_t),
\qquad
\widetilde V(t,s)=\frac{\partial V}{\partial s}(t,s).}
$$
Thus the stock holding is the claim's <option delta>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 211 / 3 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 211 / 3 / d / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 211 / 3 / d / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)